MgB2 with Tc ≈ 40 K, is a record-breaking compound among the s-p metals and alloys. It appears that this material is a rare example of the two band electronic structures, which are weakly connected with each other. Experimental results clearly reveal that boron sub-lattice conduction band is mainly responsible for superconductivity in this simple compound. Experiments such as tunneling spectroscopy, specific heat measurements, and high resolution spectroscopy show that there are two superconducting gaps. Considering a canonical two band BCS Hamiltonian containing a Fermi Surface of π- and σ-bands and following Green’s function technique and equation of motion method, we have shown that MgB2 possess two superconducting gaps. It is also pointed out that the system admits a precursor phase of Cooper pair droplets that undergoes a phase locking transition at a critical temperature below the mean field solution. Study of specific heat and density of states is also presented. The agreement between theory and experimental results for specific heat is quite convincing. The paper is organized in five sections: Introduction, Model Hamiltonian, Physical properties, Numerical calculations, Discussion and conclusions.
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